Deep Probabilistic Koopman: Long-term time-series forecasting under periodic uncertainties

TL;DR

Deep Probabilistic Koopman (DPK) offers a simple, stable, and accurate method for long-term probabilistic forecasting of complex time series across diverse domains, outperforming specialized models.

Contribution

The paper introduces DPK, a novel approach based on Koopman operator theory that enables long-term probabilistic forecasting without time stepping and with a small model size.

Findings

Outperforms 177 domain-specific models in electricity demand forecasting

Accurately predicts thousands of steps into the future across multiple domains

Demonstrates stability and calibration in long-term probabilistic predictions

Abstract

Probabilistic forecasting of complex phenomena is paramount to various scientific disciplines and applications. Despite the generality and importance of the problem, general mathematical techniques that allow for stable long-term forecasts with calibrated uncertainty measures are lacking. For most time series models, the difficulty of obtaining accurate probabilistic future time step predictions increases with the prediction horizon. In this paper, we introduce a surprisingly simple approach that characterizes time-varying distributions and enables reasonably accurate predictions thousands of timesteps into the future. This technique, which we call Deep Probabilistic Koopman (DPK), is based on recent advances in linear Koopman operator theory, and does not require time stepping for future time predictions. Koopman models also tend to have a small parameter footprint (often less than 10,000 parameters). We demonstrate the long-term forecasting performance of these models on a diversity of domains, including electricity demand forecasting, atmospheric chemistry, and neuroscience. For electricity demand modeling, our domain-agnostic technique outperforms all of 177 domain-specific competitors in the most recent Global Energy Forecasting Competition.